Answer:
= 5n - 1
Step-by-step explanation:
There is a common difference between consecutive terms , that is
9 - 4 = 14 - 9 = 19 - 14 = 5
This indicates the sequence is arithmetic with nth term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 4 and d = 5 , then
= 4 + 5(n - 1) = 4 + 5n - 5 = 5n - 1
Answer:
y = (-14/15) x + (11/15)
Explanation:
The slope-intercept form has the following formula:
y = mx + c
where:
m is the slope
c is the y-intercept
The given is:
14x + 15y = 11
To put this in slope-intercept form, we will need to isolate the y as follows:
14x + 15y = 11
15y = -14x + 11
y = (-14/15) x + (11/15)
were:
m is the slope = -14/15
c is the y-intercept = 11/15
Hope this helps :)
Answer:
a) P ( E | F ) = 0.54545
b) P ( E | F' ) = 0
Step-by-step explanation:
Given:
- 4 Coins are tossed
- Event E exactly 2 coins shows tail
- Event F at-least two coins show tail
Find:
- Find P ( E | F )
- Find P ( E | F prime )
Solution:
- The probability of head H and tail T = 0.5, and all events are independent
So,
P ( Exactly 2 T ) = ( TTHH ) + ( THHT ) + ( THTH ) + ( HTTH ) + ( HHTT) + ( HTHT) = 6*(1/2)^4 = 0.375
P ( At-least 2 T ) = P ( Exactly 2 T ) + P ( Exactly 3 T ) + P ( Exactly 4 T) = 0.375 + ( HTTT) + (THTT) + (TTHT) + (TTTH) + ( TTTT)
= 0.375 + 5*(1/2)^4 = 0.375 + 0.3125 = 0.6875
- The probabilities for each events are:
P ( E ) = 0.375
P ( F ) = 0.6875
- The Probability to get exactly two tails given that at-least 2 tails were achieved:
P ( E | F ) = P ( E & F ) / P ( F )
P ( E | F ) = 0.375 / 0.6875
P ( E | F ) = 0.54545
- The Probability to get exactly two tails given that less than 2 tails were achieved:
P ( E | F' ) = P ( E & F' ) / P ( F )
P ( E | F' ) = 0 / 0.6875
P ( E | F' ) = 0
Answer:
d. 2
Step-by-step explanation:
